Introduction to Dynamical Systems and Chaos (Summer, 2016)

About the Course:

In this course you’ll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.

Topics to be covered include: phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation. The course will focus on some of the realizations from the study of dynamical systems that are of particular relevance to complex systems:

Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system’s
behavior.

Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.

Disordered behavior can be stable. Non-periodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.

Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.

About the Instructor:

David Feldman is Professor of Physics and Mathematics at College of the Atlantic. From 2004-2009 he was a faculty member in the Santa Fe Institute’s Complex Systems Summer School in Beijing, China. He served as the school’s co-director from 2006-2009. Dave is the author of Chaos and Fractals: An Elementary Introduction (Oxford University Press, 2012), a textbook on chaos and fractals for students with a background in high school algebra. Dave was a U.S. Fulbright Lecturer in Rwanda in 2011-12.

Course dates:

5 Jul 2016 9am PDT to
20 Sep 2016 3pm PDT

Prerequisites:

A familiarity with basic high school algebra. There will be optional lessons for those with stronger math backgrounds.

Many readers often ask me for resources for delving into the basics of information theory. I hadn’t posted it before, but the Santa Fe Institute recently had an online course Introduction to Information Theory through their Complexity Explorer, which has some other excellent offerings. It included videos, fora, and other resources and was taught by the esteemed physicist and professor Seth Lloyd. There are a number of currently active students still learning and posting there.

Introduction to Information Theory

About the Tutorial:

This tutorial introduces fundamental concepts in information theory. Information theory has made considerable impact in complex systems, and has in part co-evolved with complexity science. Research areas ranging from ecology and biology to aerospace and information technology have all seen benefits from the growth of information theory.

In this tutorial, students will follow the development of information theory from bits to modern application in computing and communication. Along the way Seth Lloyd introduces valuable topics in information theory such as mutual information, boolean logic, channel capacity, and the natural relationship between information and entropy.

Lloyd coherently covers a substantial amount of material while limiting discussion of the mathematics involved. When formulas or derivations are considered, Lloyd describes the mathematics such that less advanced math students will find the tutorial accessible. Prerequisites for this tutorial are an understanding of logarithms, and at least a year of high-school algebra.

About the Instructor(s):

Professor Seth Lloyd is a principal investigator in the Research Laboratory of Electronics (RLE) at the Massachusetts Institute of Technology (MIT). He received his A.B. from Harvard College in 1982, the Certificate of Advanced Study in Mathematics (Part III) and an M. Phil. in Philosophy of Science from Cambridge University in 1983 and 1984 under a Marshall Fellowship, and a Ph.D. in Physics in 1988 from Rockefeller University under the supervision of Professor Heinz Pagels.

From 1988 to 1991, Professor Lloyd was a postdoctoral fellow in the High Energy Physics Department at the California Institute of Technology, where he worked with Professor Murray Gell-Mann on applications of information to quantum-mechanical systems. From 1991 to 1994, he was a postdoctoral fellow at Los Alamos National Laboratory, where he worked at the Center for Nonlinear Systems on quantum computation. In 1994, he joined the faculty of the Department of Mechanical Engineering at MIT. Since 1988, Professor Lloyd has also been an adjunct faculty member at the Sante Fe Institute.

Professor Lloyd has performed seminal work in the fields of quantum computation and quantum communications, including proposing the first technologically feasible design for a quantum computer, demonstrating the viability of quantum analog computation, proving quantum analogs of Shannon’s noisy channel theorem, and designing novel methods for quantum error correction and noise reduction.

Professor Lloyd is a member of the American Physical Society and the Amercian Society of Mechanical Engineers.

Tutorial Team:

Yoav Kallus is an Omidyar Fellow at the Santa Fe Institute. His research at the boundary of statistical physics and geometry looks at how and when simple interactions lead to the formation of complex order in materials and when preferred local order leads to system-wide disorder. Yoav holds a B.Sc. in physics from Rice University and a Ph.D. in physics from Cornell University. Before joining the Santa Fe Institute, Yoav was a postdoctoral fellow at the Princeton Center for Theoretical Science in Princeton University.

I know many people who could identify a fake Louis Vuitton (LVMH) purse, a knock off Christian Louboutin, or a sham Rolex, but who simultaneously are overly religious about their food brands and topics like organic food and couldn’t similarly identify the fakes they’re eating because of fraud in food labeling and misdirection and legerdemain within the food supply chain. Finally there’s a course to help everyone become smarter consumers.

The food industry is one of the most important commercial sectors in the world. Everyone uses it, but how many people abuse it? As we witness the increasing globalisation of the supply chain, a growing challenge is verifying the questionable identity of raw materials in the food we eat.

In this course we will look at topical issues concerning ‘food fraud’ and explore ways in which analytical chemistry can help in its identification and prevention. We’ll share fascinating examples, such as the history of white bread and a surprising ingredient once found in bitter beer.

The University of East Anglia has joined forces with the world-renowned Institute of Food Research (IFR) to bring you this unique course. You’ll be led by Kate Kemsley, a specialist in the use of advanced instrumentation for measuring the chemical composition of food materials. Course content is linked with UEA’s MChem postgraduate programme, which supports final-year students’ practical research projects in this area of science.